Perfect 3-Colorings of the Johnson Graph J (6, 3)

Under a perfect coloring with m colors (a perfect m -coloring) with matrix A={a_ij}_i,j=1,… ,m of a graph G , we understand a coloring of the vertices G with the colors {1,… ,m} such that the number of vertices of color j adjacent to a fixed vertex of color i is equal to a_ij independently of the choice of the latter vertex. The matrix A is called the parameter matrix of a perfect coloring. This paper introduces the method breaking, the inverse of merging, which produces sufficient constructions for the paper. Furthermore, the parameter matrices of all perfect 3-colorings of the Johnson graph J (6, 3) are enumerated.